Welcome back! Glad that you’ve decided to stick around for the Second Rights of the Learner: The Right to Claim a Mistake and Revise Your Thinking. This right is one that I’ve struggled with how to frame over the past year because my thinking has evolved and I’ll briefly go into that here just for full transparency.
When I first learned about the RotL from Olga Torres (which back then was simply “The right to make a mistake”), I really liked the second RotL because it was one that I saw my students desperately trying to avoid. Some of my students would break their backs to be careful with what they said and wrote as to not make a “mistake” or misstep in their mathematical thinking. And if they did, they sure weren’t ever going to admit it to me. We as teachers have learned the practice of intentionally posing “a mistake” in our public work on the board for students to catch and say “MISS!! YOU MADE A MISTAKE” That strategy can normalize mistakes as something that we all do and it’s ok. But what I’ve recently struggled with is what constitutes a mistake and why are teachers the ones to name it “a mistake?” (I appreciate my equity-minded colleagues helping me to think more about this because over the years I’ve noticed how sharper my awareness is for noticing the language that I use and the implications those words have with my students.)
So what’s “wrong” with teachers saying or naming something as a mistake? What if we returned to Gretchen in First RotL post and told her she made “a mistake” when she wrote 53 as the answer to 70-23? How do you think a 3rd grader might have reacted to hearing that: Maybe shock? Embarrassment? Withdrawing herself to no longer feel safe to offer her thinking? Nothing of it? Rochelle Gutierrez and others like Julia Aguirre have written and presented about how we in mathematics education need to move away from language like “mistakes, misconceptions, mis[insert another word].” Why? Because when we say “mistake, misconception, misstep” we as teachers in power are making the assumption that what the child said was wrong or that the thinking resides in a space of incorrectness. What if Gretchen truly and honestly believed that 70-23 was 53 and that this wasn’t a mistake? What does telling her she made a mistake and that the answer is 47 mean for her as a math student/learner/thinker? It’s taken me a while to get to a place where I can see what Gutierrez and other’s have been talking about. Naming a child’s thinking as a mistake or misconception treads into the shallow end of deficit thinking and could lead teachers to start naming right/wrong answers that might also lead to shutting kids down when their answer doesn’t match up with what the teacher/book says.
On the other hand, I am not advocating for avoiding the words mistake or misconceptions. I mean, TBH, I’ve published work that has those words. I gotta own that. But it should come from the student first, not the teacher. For me, it’s ok for kid to say “WHOOPSIE DAISY! I didn’t meant to do that. I made a mistake, Miss.” as opposed to me calling a kid out for one before they have had the chance to see it and name it as such.
So let kids claim a mistake and also give them the opportunity to revise their thinking and engage in Rough Draft Talk (Jansen, Cooper, Vascellaro, & Wandless, 2017). In math, nothing should be set in stone… unless you’re still doing your math homework on stone tablets. Then you’re kinda stuck with that one.
Now that we have that settled (for now), why are mistakes important in math class? Because again they serve as a window into student thinking (Hiebert & Grouws, 2007)! And don’t we as teachers want to know more about how our students are thinking, aside from right or wrong answers? (The answer is yes, BTW).
This second right is a perfect opportunity for teachers to pose open-ended tasks that encourage divergent formative assessments. Teachers who use open-ended tasks (no clear answer or solution method, multiple solutions or justifications, can be extended up and down based on child’s experience with math) and divergent formative assessments step into a place of curiosity: WHAT do my kids know about this task versus IF they learned or mastered the material? They not only tell you more about how the child is thinking about the task itself, but also maybe about the micro-level of operating on numbers. Gretchen’s scenario helps us to know more about how she is thinking about 0-3 AND her knowledge of base ten AND how she’s using different methods to confirm or disprove her answers. If she simply looked up at the interviewer and said, “53” well… that tells us she answered the question, but not much else.
So ultimately, embrace mistakes. We make them. Own them. Name them. Shine a light on them. Learn from them. Because you never know what might become of those mistakes later on…
Hiebert, J., & Grouws, D. (2007). The effects of classroom mathematics teaching on student learning. Charlotte, NC: Information Age Publishers.
Jansen, A., Cooper, B., Vascellaro, S., & Wandless, P. (2017). Rough-Draft Talk inMathematics Classrooms. Mathematics Teaching in the Middle School, 22(5), 304-307.